I really applaud you for telling your wife. I know that was not easy. I'm so glad that she responded in such a positive way.
I think others here have given you great advice, and it sounds like you are taking all the steps necessary to get the help you need. I'm no psychologist, but I suspect your anger stems in part from the helplessness you feel. I think addiction is especially hard for Christians, because we can't help but to equate it with sin. So we try to "pray our way through it," and we still feel overpowered. Then we start questioning our faith, and even begin to question God.
But addiction is somehow something completely separate from sin. Yes, sin may have led us to our addictive state, but once we are addicted it becomes more than solely a spiritual issue. We can no longer "pray our way through it." As Hiwot said, a holistic approach is required. And knowing you like I think I do, I am confident that you will continue to cultivate your spiritual life as you seek other aspects of treatment and help.
Stop worrying about letting other people down. You are in a fight for your life, and there is no shame in your struggle. If others are "disappointed" in you, then the shame is theirs not yours.
I love you brother, and my prayers are with you.